Page 416 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

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Encyclopedia of Physical Science and Technology EN012C-568 July 26, 2001 15:32

66 Photoelectron Spectroscopy

FIGURE 8 Orbital representation of (a) the initial and (b–f) different final states of the photoemission process.

of systems with such a ground state. It is an exception one of the occupied orbitals without disturbing the remain-
for atoms but is very common for molecules. Apart from ing electrons. This is called the “frozen orbital approxima-
the orbitals that are occupied in the ground state, there tion” (FOA). This process creates a hole in the manifold
are unoccupied or “virtual” orbitals. For example, for the of the occupied orbitals, and we call the resulting state a
6
2
2
neon atom, with a ground state configuration 1s 2s 2p , “hole state.” If the electron is removed from the highest
the lowest unoccupied orbital is 3s. In the following dis- occupied orbital, the final state of the photoemission pro-
cussion, it is important to keep in mind that “occupied” cess is the ground state M + of the ion (Fig. 8b). If the
0
always refers to the set of orbitals occupied in the ground electron is removed from a lower lying orbital, an excited
state M 0 . Correspondingly, “unoccupied” always refers to state of the ion is reached which we call a “hole excited
the set of orbitals not occupied in the ground state. state” because moving a hole downward is the same as
When we turn from atoms to molecules, the situation moving an electron upward (Fig. 8c). When the electron
changes only slightly. The major difference is that the is removed from a core orbital, we speak of a “core hole
valence orbitals no longer belong to a single atom. To a state” (Fig. 8d). Such a state is usually labeled by the
greater or lesser degree, they are extended over the whole chemical symbol of the atom and the orbital from which
molecule. The same is true for the unoccupied orbitals. the electron has been removed (e.g., C 1s,O1s,P2p).
The core orbitals are still localized at their respective If we start from M + (Fig. 8b) and excite one of the
0
atoms. Degenerate valence orbitals are less common in remaining electrons to an unoccupied orbital (Fig. 8e),
molecules than in atoms; they are usually found in mole- a new type of excited ion state is reached. Compared to
cules of higher symmetry with at least one three-fold axis. the ground state M 0 of the initial system, this state has
For solids, the number of atoms and therefore the two holes in the occupied orbitals and one electron in an
number of orbitals goes to infinity. The valence orbitals unoccupied orbital. Therefore, it is called a “two-hole one-
develop into continuous energy bands. The details of the particle (2h1p) state.” Analogously, we can define three-
electronic structure of a crystalline solid are described in hole two-particle states, and so on.
terms of the “band structure.” The energy up to which the
bands are occupied is the Fermi energy (E F ) already men-
tioned in Section I.E. When the Fermi energy lies within C. Secondary Structures in PE Spectra
a band, the solid is a metal; when it lies in a gap between
The nh(n-1)p states are frequently called “shake-up
two bands, the solid is a semiconductor (small gap) or
states,” based on the idea that photoionization is such
an insulator (large gap). As in molecules, the core orbitals
a strong perturbation that the whole electron system is
in solids still behave like those in atoms.
“shaken” and one or more of the remaining electrons are
“shaken up” to unoccupied orbitals. If the “shake-up elec-
B. The Frozen Orbital Approximation
tron” receives enough energy to leave the system, the final
We now return to photoemission. For a first approxima- state of the photoionization is a state of the doubly ion-
tion, we assume that we can remove a single electron from ized system (Fig. 8f). This type of transition was shown as